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Simplifying 5 + 3(1 + 4j) = -32 5 + (1 * 3 + 4j * 3) = -32 5 + (3 + 12j) = -32 Combine like terms: 5 + 3 = 8 8 + 12j = -32 Solving 8 + 12j = -32 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 12j = -32 + -8 Combine like terms: 8 + -8 = 0 0 + 12j = -32 + -8 12j = -32 + -8 Combine like terms: -32 + -8 = -40 12j = -40 Divide each side by '12'. j = -3.333333333 Simplifying j = -3.333333333
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